Question

Consider the population of four juvenile condors. Their weights in pounds are : 2, 3, 6, 10 (a) Let x be the weight of a juvenile condor. Write the possible unique values for x: (NOTE: Separate each value in the list with a comma.) ANS = 2,3,6,10 (b) Find the mean of the population: ANS = 5.25 (c) Let x¯ be the average weight from a sample of two juvenile condors. List all possible outcomes for x¯. (If a value occurs twice, make sure to list it twice.) This is the sampling distribution for samples of size 2: (NOTE: Separate each value in the list with a comma.) ? (d) Find the mean of the sampling distribution: ?

Answer 1

c)

Sample	Average weight
(2,2)	2
(2,3)	2.5
(2,6)	4
(2,10)	6
(3,2)	2.5
(3,3)	3
(3,6)	4.5
(3,10)	6.5
(6,2)	4
(6,3)	4.5
(6,6)	6
(6,10)	8
(10,2)	6
(10,3)	6.5
(10,6)	8
(10,10)	10

The sampling distribution for samples of size 2: 2, 2,5, 2,5, 3, 4, 4, 4.5, 4.5, 6, 6, 6, 6.5, 6.5, 8, 8, 10

d)

Sample mean	Probability
2	1/16 = 0.0625
2.5	2/16 = 0.125
3	1/16 = 0.0625
4	2/16 = 0.125
4.5	2/16 = 0.125
6	3/16 = 0.1875
6.5	2/16 = 0.125
8	2/16 = 0.125
10	1/16 = 0.0625

mean of the sampling distribution = 2 * 1/16 + 2.5 * 2/16 + 3 * 1/16 + 4 * 2/16 + 4.5 * 2/16 + 6 * 3/16 + 6.5 * 2/16 + 8 * 2/16 + 10 * 1/16 = 5.25